We consider a contextual Markov Decision Process [1]}, [2]} \(\mathcal {M}_z\)  parameterized with respect to a context \(z\) , where the state space, action space, reward function, and the environment all depend on \(z\) . Here we define \(z\)  to be the parameters of the input MIP, i.e., \(z = M = \lbrace A, b, c\rbrace \) . The state \(s_t\)  at the \(t^{th}\)  step of an episode is the current assignment \(x_t\)  of values for all the integer variables in \(M\) . The action \(a_t \in \lbrace 0,1\rbrace ^{|\mathcal {I}|}\)  at step \(t\)  is the choice of the set of integer variables to be unassigned, specified by one indicator variable per integer variable in \(M\)  where 1 means unassigned. All continuous variables are labelled as unassigned at every LNS step. For real-world applications the number of integer variables \(|\mathcal {I}|\)  is typically large (\(10^3-10^6\) ), so the actions are high-dimensional binary vectors. The policy \(\pi _{\theta }(a_t | s_t, M)\)  defines the distribution over actions, parameterized by \(\theta \) . We use a conditional generative model to represent this high-dimensional distribution over binary vectors (section REF ).
